Evolutionary dynamics in games imply de-facto spiteful behavior of the players: In order to 'survive' the evolutionary process, players must perform better than their opponents. This means they maximize relative rather than absolute payoffs. The paper shows that there is a class of games resulting in different equilibria if played by maximizers of absolute or of relative pay-offs, respectively. It is demonstrated that evolutionary equilibria (general ESS) can be found by formally maximizing relative payoffs. This method is analytically deduced and demonstrated at the examples of four well known games: the Cournot oligopoly game, the public goods game, the Tullock game of rent seeking and the Van Huyck et al. (1990) coordination game.